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- W2963508744 abstract "Let $A$ be a Koszul (or more generally, $N$-Koszul) Calabi-Yau algebra. Inspired by the works of Kontsevich, Ginzburg and Van den Bergh, we show that there is a derived non-commutative Poisson structure on $A$, which induces a graded Lie algebra structure on the cyclic homology of $A$; moreover, we show that the Hochschild homology of $A$ is a Lie module over the cyclic homology and the Connes long exact sequence is in fact a sequence of Lie modules. Finally, we show that the Leibniz-Loday bracket associated to the derived non-commutative Poisson structure on $A$ is naturally mapped to the Gerstenhaber bracket on the Hochschild cohomology of its Koszul dual algebra and hence on that of $A$ itself. Relations with some other brackets in literature are also discussed and several examples are given in detail." @default.
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- W2963508744 date "2017-01-01" @default.
- W2963508744 modified "2023-10-16" @default.
- W2963508744 title "The derived non-commutative Poisson bracket on Koszul Calabi–Yau algebras" @default.
- W2963508744 doi "https://doi.org/10.4171/jncg/11-1-4" @default.
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